Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 16 (2021), 259 -- 274

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ON A GENERALIZATION OF EULER'S CONSTANT

Stephen Kaczkowski

Abstract. A one parameter generalization of Euler's constant γ from [Numer. Algorithms 46(2) (2007) 141--151] is investigated, and additional expressions for γ are derived. Included are forms involving the Gregory coefficients and the Hurwitz Zeta function, and expressions of the later are shown to lead to an alternative proof of Lerch's limit formula for the gamma function.

2020 Mathematics Subject Classification: 30B10; 33B15; 11M35; 30E20; 11M06
Keywords: Euler's Constant; Gamma Function; Hurwitz Zeta Function

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Stephen Kaczkowski
South Carolina Governor's School for Science and Mathematics,
401 Railroad Avenue
Hartsville, SC 29550 USA.
e-mail: s.v.kaczkowski@gmail.com



http://www.utgjiu.ro/math/sma